GEOMETRY Name: ________________________ Reasoning Activity – CHP. 2 Hour: _________ REASONING in LITERATURE Watch a short video clip from “Alice in Wonderland” : http://www.youtube.com/watch?v=1oupIOmnLJs&feature=player_embedded • Watch for “awkward sayings”, instances of deductive/inductive reasoning, uses of Law of Detachment, or Law of Syllogism. Consider the following passage from Lewis Carroll’s Alice’s Adventures in Wonderland, Chapter VII, “A Mad Tea Party.” "Then you should say what you mean." the March Hare went on. "I do," Alice hastily replied; "at least -- at least I mean what I say -- that's the same thing, you know." "Not the same thing a bit!" said the Hatter, "Why, you might just as well say that 'I see what I eat' is the same thing as 'I eat what I see'!" "You might just as well say," added the March Hare, "that 'I like what I get' is the same thing as 'I get what I like'!" "You might just as well say," added the Dormouse, who seemed to be talking in his sleep, "that 'I breathe when I sleep' is the same thing as 'I sleep when I breathe'!" "It is the same thing with you," said the Hatter, and here the conversation dropped, and the party sat silent for a minute. Lewis Carroll, the author of Alice in Wonderland and Through the Looking Glass, was a mathematics teacher who had fun playing around with logic. In this activity, you’ll investigate some basic ideas from logic and perhaps have some fun too. 1. Express each of the following statements from the Mad Tea Party as a CONDITIONAL in “if … then” form, CONVERSE, INVERSE and CONTRA POSTIVE. Give the TRUTH VALUE of EACH STATEMENT. Write as a BICONDITIIONAL and indicate it’s TRUTH VALUE. a. I like what I get. (Try using the flow chart method of organizing your information.) Converse Bi-Conditional Q -> P P iff Q Conditional P->Q Inverse ~P -> ~Q Contra Positive ~Q -> ~P b. I breathe when I sleep. CONDITIONAL: ___________________________________________________________________ CONVERSE: ______________________________________________________________________ INVERSE: ________________________________________________________________________ CONTRA POSITIVE: _______________________________________________________________ BICONDITIONAL: _________________________________________________________________ c. I see what I eat. CONDITIONAL: ___________________________________________________________________ CONVERSE: ______________________________________________________________________ INVERSE: ________________________________________________________________________ CONTRA POSITIVE: _______________________________________________________________ BICONDITIONAL: _________________________________________________________________ d. I mean what I say. (Try using the flow chart method of organizing your information.) Converse Bi-Conditional Q -> P P iff Q Conditional P->Q Inverse ~P -> ~Q Contra Positive ~Q -> ~P 2. The March Hare, Hatter, and Dormouse did not use “if … then” form when they stated their conditionals. Write the converse for each conditional statement below without using “if … then” form. Conditional: I breathe when I sleep. Converse: ________________________________________ Conditional: I like what I get. Converse: ________________________________________ Conditional: I see what I eat. Converse: ________________________________________ Conditional: I say what I mean. Converse: ________________________________________ 3 . When Alice first meets the Cheshire Cat, she asks what sort of people live in Wonderland. The Cat explains that everyone in Wonderland is mad. What conjecture might the Cat make since Alice, too, is in Wonderland? Is this an example of DEDUCTIVE or INDUCTIVE reasoning? Explain. CONJECTURE:___________ ____________________________________________________________ DEDCUTIVE or INDUCTIVE? Explain.____________________________________________________ _____________________________________________________________________________________ 4. Write the CONDITIONAL STATEMENT implied by the cat’s response to Alice: “I don’t much care where—” said Alice. “Then it doesn’t matter which way you go,” said the Cat. “—so long as I get somewhere,” Alice added as an explanation. “Oh, you’re sure to do that,” said the Cat, “if you only walk long enough.” CONDITIONAL: _____________________________________________________________________ 5. Is the cat’s conclusion valid by LAW OF DETACHMENT or LAW OF SYLLOGISM? Explain your reasoning. “Well, then,” the Cat went on, “you see a dog growls when it’s angry, and wags its tail when it’s pleased. Now I growl when I’m pleased, and wag my tail when I’m angry. Therefore I’m mad.” VALID or INVALID: explain ____________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 6. Is Alice’s CONCLUSION VALID using the LAW OF DETACHMENT? Explain your reasoning. Alice: “If TIME stopped time for you, he could stop time for me? Mad Hatter: “He only stops time at tea time.” Alice: “SO then it’s always tea time there?” VALID or INVALID: explain ____________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ .